Numerical solution for the anisotropic Willmore flow of graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00222650" target="_blank" >RIV/68407700:21340/15:00222650 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.apnum.2014.10.001" target="_blank" >http://dx.doi.org/10.1016/j.apnum.2014.10.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apnum.2014.10.001" target="_blank" >10.1016/j.apnum.2014.10.001</a>

Result language
angličtina
Original language name
Numerical solution for the anisotropic Willmore flow of graphs
Original language description
The Willmore flow is well known problem from the differential geometry. It minimizes the Willmore functional defined as integral of the mean-curvature square over given manifold. For the graph formulation, we derive modification of the Willmore flow withanisotropic mean curvature. We define the weak solution and we prove an energy equality. We approximate the solution numerically by the complementary finite volume method. To show the stability, we re-formulate the resulting scheme in terms of the finite difference method. By using simple framework of the finite difference method (FDM) we show discrete version of the energy equality. The time discretization is done by the method of lines and the resulting system of ODEs is solved by the Runge?Kutta?Merson solver with adaptive integration step. We also show experimental order of convergence as well as results of the numerical experiments, both for several different anisotropies.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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